The buckling of magnetically saturated elastic bodies in an external magnetic field is discussed. A linearized version of the general nonlinear equations for the magnetoelastic interactions in magnetically saturated bodies is presented, from which a buckling criterion is derived. This criterion is applied in two examples, viz. a thin plate and a circular rod. Results obtained are compared with those for soft ferromagnetic bodies, as known in the literature. It turns out that, although the descriptions are essentially different, the final results for the saturation model and for the soft magnetic model are in good correspondence with one another.